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The properties of symmetric nuclear matter are investigated in the nonlinear relativistic mean field theory of nuclear matter. We consider the constraints imposed by four nuclear ground state properties on the coupling constants and on the equation of state at zero and at finite temperature. We find that the compression constant K(&#961;0) as well as the temperature is irrelevant for the stiffness of the equation of state for m*(&#961;0)&#8804;0.7. The main point is that the relativistic mean field theory exhibits acausal and unphysical behavior for compressibilities below K(&#961;0)=200 MeV. Every set of coupling constants with a negative quartic coupling constant c is unstable against small quantum fluctuations.

We analyze the phase structure of the nonlinear mean-field meson theory of baryonic matter (nucleons plus delta resonances). Depending on the choice of the coupling constants, we find three physically distinct phase transitions in this theory: a nucleonic liquid-gas transition in the low temperature, Tc<20 MeV, low density, &#961;&#8771;0.5&#961;0, regime, a high-temperature (T&#8771;150 MeV) finite density transition from a gas of massive hadrons to a nearly massless baryon, antibaryon plasma, and, third, a strong phase transition from the nucleonic fluid to a resonance-dominated ‘‘delta-matter’’ isomer at &#961;>2&#961;0 and Tc<50 MeV. All three phase transitions are of first order. It is shown that the occurrence of these different phase transitions depends critically on the coupling constants. Since the production of pions also depends strongly on the coupling constants, it is seen that the equation of state cannot be derived unambiguously from pion data.